Explain Red-Black tree properties and why they guarantee O(log n) operations.

Red-Black trees are self-balancing BSTs with five properties: nodes are red or black, root is black, leaves (NIL) are black, red nodes have black children, and all paths from node to descendant leaves have equal black nodes. These properties ensure the longest path is at most twice the shortest (alternating red-black vs all black), guaranteeing height <= 2log(n+1). Rebalancing uses rotations and recoloring after insert/delete.